Q 42 - Calculus

Question

Each of the integrals or integral expressions in Exercises $38-44$ represents the area of a region in the plane. Use polar coordinates to sketch the region and evaluate the expressions.

$3{\int }_0^{\mathrm{\pi }/2}{\sin }^{2}3\theta d\theta$.

Step-by-Step Solution

Answer

The required graph is :-

Step 1: Interpret the integral geometrically

The integral expression represents the area of a region in the plane. Identify the curves that bound the region from the integrand and limits.

Step 2: Sketch the region

Graph the bounding curves and shade the enclosed region to visualize the area represented by the integral.